Index Numbers: The CPI
Friday January 14, 2011
(continued)
What is an Index Number?
•
An
index number
provides a simple way to compare measurements made at di
ff
erent
times or in di
ff
erent places.
The value at one particular time (or place) must be
chosedn as the reference value. The index number for any other times (or place) is
index number =
value
reference value
×
100
(1)
Wednesday January 1, 2011
Example 1.
Consider the average gas prices by year as given below:
Year
Price (in cents)
Price as a percentage
of 1975 price
Price
index
(1975 = 100)
1955
29.1
51.3%
51.3
1965
31.2
55.0%
55.0
1975
56.7
100.0%
100.0
1985
119.6
210.9%
210.9
1995
120.5
212.5%
212.5
2005
231.0
407.4%
407.4
Here we have chosen the 1975 price to be the reference value (i.e.
all other prices are
compared to the 1975 price in the last two columns).
The percentages and indices were
computed using (1) as follows:
1955price
1975price
=
29
.
1cents
56
.
7cents
= 0
.
513 = 51
.
3%
Therefore the index number for the 1955 gas price using the 1975 gas price as the reference
value is 51.3.
The indices for the gas prices in other years is computed similarly.
1
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1.
Making Comparisons with Index numbers
Main purpose for index numbers is to facilitate comparisons.
Example 2.
Using the table above we can easily compare gas prices in various years
to the gas price in 1975. For example, the index for 1995 is 121.5. This means that
the price of gas in 1995 was 212.5%
of
the price of gas in 1975. Equivalently, the 1995
price was 2.12 times the 1975 price.
Example 3.
Using the above table for gas prices, we can also compare two gas prices
when neither of the two prices is the reference price. Suppose we want to know how
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 Spring '08
 Staff
 Inflation, 1920, 1921, 1911, Consumer price index, January 1

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